Abstract: An expected volume coefficient (EV) is defined and proposed to displace volume and selectivity as criteria for the evaluation of confidence sets, and a proposal for evaluation is given. This proposal addresses anomolies that occur with sets based on discrete probability distributions; for example, that classical exact confidence intervals are wider than approximate ones. Options for the other key criterion, coverage, range from attaining average coverage, a liberal (i.e., leading to smaller sets ) criterion, to attaining coverage for all values of the unknown parameter and al l sample sizes, a very conservative criterion for sets based on discrete distributions. Use of EV is demonstrated with two-sided confidence intervals for the binomial probability parameter, leading to new recommendations; in particular, a Wald logit interval with negative continuity correction.
Key words and phrases: Average coverage, binomial proportion, confidence intervals, continuity correction, coverage, expected volume, expected width, logit, Neyman shortness, selectivity.